A measure that would repeal caps on annual increases in military retired pay steamed through the House on Tuesday, receiving well over the two-thirds majority required for fast-tracked legislation.

The vote was 326-90.

After announcing earlier in the day they would not tie repeal of the caps on cost-of-living adjustments for retirees to broader legislation to suspend the federal debt ceiling, House Republican leaders then forwarded an amendment on COLA cap repeal as a rider to another unrelated bill that has already been approved by the Senate.

The COLA caps are estimated to save $6 billion over 10 years. The House’s repeal provision would offset the lost savings by extending sequestration on mandatory Medicare spending by one year, to 2024.

Prior to the vote, House Armed Services Committee member Rep. Adam Smith, D-Wash., said he could not support a measure that pits one group against another for funding support — in this case, Medicare-eligible seniors versus military retirees.

House Minority Whip Rep. Steny Hoyer, D-Md., told the Hill newspaper he would vote against the bill because of the Medicare offset, an arrangement that he said would undermine efforts for long-term spending reform.

The Senate is poised to consider its own legislation to repeal the COLA caps. That provision cleared a key procedural hurdle Monday, although it does not include any proposal for offsetting the $6 billion in lost savings.

Senators voted unanimously, 94-0, to advance that bill, drafted by Sen. Mark Pryor, D-Ark. Debate on that bill is underway, and senators can offer amendments to offset the lost savings. A vote could come as early as Wednesday.

Either piece of legislation, if approved by both chambers, would undo a section of a previous federal budget deal that wold have reduced annual COLA increases by 1 percentage point for “working age” retirees under 62, starting in late 2015.

House lawmakers moved swiftly on Tuesday to voice support for their legislation.

“It is imperative that we keep our promise to the members of the armed services who have sacrificed so much for our country,” said Rep. Gus Bilirakis, R-Fla.. “Military retirees have bravely served and made enormous personal sacrifices. Our country promised these retirement pensions to military retirees. I am pleased to see that Congress is able to honor that commitment.”